Method and apparatus for reducing crosstalk interference in an inline Fabry-Perot sensor array

ABSTRACT

A method and apparatus for reducing crosstalk between sensors in an inline Fabry-Perot (FP) sensor array. The inline FP sensor array comprises a plurality of fiber Bragg gratings arranged periodically along an optical fiber. The sensors are formed between each of the Bragg gratings. A light source provides multiplexed pulses as interrogation pulses for the array. The light pulses are applied to one end of the sensor array and a light detector detects reflected pulses. The detected pulses comprise a composite of reflections from all the Bragg gratings along the fiber. The apparatus processes the detected signals using an inverse scattering algorithm to detect an accurate phase response from each of the Bragg sensors while reducing crosstalk from other Bragg sensors within the array. One form of inverse scattering algorithm is a layer-peeling algorithm.

This application contains subject matter that is related to the subjectmatter described in U.S. patent application Ser. No. ______, filedsimultaneously herewith (Attorney docket number WEAT 0347) and U.S.patent application Ser. No. ______, filed simultaneously herewith(Attorney docket number WEAT 0493), which are both incorporated hereinby reference in their entirety.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to optical signal processing techniquesand, in particular, the present invention relates to a method andapparatus for reducing crosstalk interference in an inline Fabry-Perotsensor array.

2. Description of the Background Art

Inline fiber optic sensor arrays based on partial reflectors such asfiber Bragg gratings (FBGs) are simple and efficient since thereflectors can be written directly into the fiber and no othercomponents are required. An inline sensor consists of two reflectorshaving a length of the fiber between the reflectors. In operation, thefiber changes through mechanical stress making the fiber sensitive tophysical or chemical measurands. Such changes in the physical attributesof the fiber will alter the light propagation characteristics of thefiber.

Time division multiplexing (TDM) of the sensor array interrogationsignals is achieved using a pulsed light source. The reflected pulsesfrom the sensors are distributed in time since the sensors are spatiallydistributed along the array. It is required that the reflections fromthe different sensors are separable in the time domain to achieve anaccurate reading of the light reflected from each sensor along thearray.

To have all the sensors along one fiber is not a favorable configurationin terms of crosstalk. There will be pulses that are reflected three oran odd number of times (higher order reflections) that coincide withpulses reflected only once (first order reflection). In existing TDMsensor systems, the phases of the sensors are calculated assuminginterference between first order reflections only. Thus, interferencebetween a first order reflection and a higher order reflection willappear as crosstalk. High-resolution sensor systems typically require acrosstalk level less than −60 dB. In order to have a crosstalk levelless than −60 dB, the reflectance of the reflectors must be less than0.1%. With such a low level of reflectance, very little of the sourcepower is utilized to provide a measurable signal. As such, crosstalknoise can substantially impact the detectability of the reflectedsignal.

Therefore, there is a need in the art for a method and apparatus thatreduces crosstalk interference in an inline Fabry-Perot sensor array.

SUMMARY OF THE INVENTION

The invention provides a method and apparatus for reducing crosstalkinterference between sensors in an inline Fabry-Perot (FP) sensor array.The inline FP sensor array comprises a plurality of partial reflectorssuch as fiber Bragg gratings arranged periodically along an opticalfiber. A light source provides multiplexed pulses as interrogationpulses for the array. The light pulses are applied to one end of thesensor array and a light detector detects reflected pulses. The detectedpulses comprise a composite of reflections from all the partialreflectors along the fiber. The invention processes the detected signalsusing an inverse scattering algorithm to detect an accurate transmissionphase delay response between each pair of subsequent reflectors whilereducing crosstalk from other reflectors within the array. One form ofinverse scattering algorithm is the layer-peeling algorithm.

BRIEF DESCRIPTION OF THE DRAWINGS

So that the manner in which the above recited features of the presentinvention are attained and can be understood in detail, a moreparticular description of the invention, briefly summarized above, maybe had by reference to the embodiments thereof which are illustrated inthe appended drawings.

It is to be noted, however, that the appended drawings illustrate onlytypical embodiments of this invention and are therefore not to beconsidered limiting of its scope, for the invention may admit to otherequally effective embodiments.

FIG. 1 depicts a block diagram of an inline Fabry-Perot sensor arraysystem;

FIG. 2 depicts the interrogation pulse sequence and reflected pulsesequence that is produced by an inline Fabry-Perot sensor array;

FIG. 3 depicts a flow diagram of a process for utilizing a Fabry-Perotsensor array in accordance with the present invention;

FIG. 4 depicts simulation results of using the present invention forproviding low crosstalk signal responses; and

FIG. 5 depicts a frequency-division multiplexed (FDM) inline Fabry-Perotsensor array.

DETAILED DESCRIPTION

FIG. 1 depicts an inline Fabry-Perot (FP) sensor array system inaccordance with the present invention. The system 100 comprises a sensorarray 102, a light source 104, a light detector 106 a sample-and-hold(S/H) circuit 126, and analog-to-digital (A/D) circuit 128, and acontroller 108. The sensor array further comprises a fiber optic cable110 and a plurality of fiber Bragg gratings (FBGs) 112 ₀, 112 ₁, 112 ₂,112 ₃, 112 ₄ and so on (also referred to as reflectors), that are eachperiodically positioned along the fiber 110. The use of four FBGs isonly illustrative, those skilled in the art will realize that any numberof FBGs may be used. The light source 104 provides interrogation pulsesthat propagate along the fiber cable. A small percentage of theinterrogation pulse energy is reflected by each of the Bragg gratings112 ₀ through 112 ₄ along the fiber. The reflected light propagatesalong the fiber cable in the opposite direction of the propagation ofthe interrogation pulse and is detected by light detector 106. Thesignal from the light detector is sampled by the S/H circuit 126 and theoutput of the S/H circuit 126 is digitized by the A/D circuit 128. Thecontroller 108 controls the timing of the interrogation pulses as wellas processes the digitized signals from the light detector. Although theembodiment shown has a single controller for controlling both the lightsource 104 and the light detector 106 as well as processing signals fromthe light detector, those skilled in the art will understand thatseparate controllers and signal processors could be used for eachfunction.

The controller comprises a central processing unit 114, support circuits116 and memory 118. The CPU 114 may comprise a general processingcomputer, microprocessor, or digital signal processor of a type that isused for signal processing. The support circuits 116 comprise well knowncircuits such as cache, clock circuits, power supplies, input/outputcircuits, and the like. The memory 118 may comprise read only memory,random access memory, disk drive memory, removable storage and otherforms of digital memory in various combinations. The memory storescontrol software 120 and signal processing software 122. The controlsoftware 120 is generally used to provide timing control of the lightsource 104 and for controlling the light detector 106. The signalprocessing software 122 is used to process the light detection output toeliminate crosstalk from higher order reflections in accordance with theinvention.

The sensor array 102 comprises N+1 reflectors 112 with fiber sections110 ₁, 110 ₂, 110 ₃ and 110₄ between the reflectors 112. Each of thesefiber sections 110 ₁ through 110₄ forms a sensor. As such, the N+1reflectors will form N sensors in the sensor array 102. FIG. 1illustratively depicts five reflectors 112 ₀ through 112₄ and foursensors 110 ₁ through 110₄. For this sensor group all the fiber withinthe group is a part of a sensor. In other arrays, some of the fiber maynot form part of a sensor.

In the array 102, there will be a small fraction of the interrogationpulse energy that is reflected more than once within the sensor group.All such multiple reflections that have a time delay shorter than thetime delay to the last reflector will appear as crosstalk, however thecrosstalk can be removed by an inverse scattering algorithm such as thelayer-peeling algorithm. The layer-peeling algorithm is one of the mostefficient inverse scattering algorithms. The signal processing softwareuses the layer-peeling algorithm to eliminate crosstalk from the signalsreceived by the light detector 106 such that an accurate phase responsefrom the sensors within the sensor array is detectable.

The layer-peeling algorithm has been used to analyze transmission lines,vibration strings, layered acoustic media, particle scattering inquantum mechanics and synthesis and spatial characterization of fiberBragg gratings. One version of the layer-peeling algorithm calculatesthe spatial profile of a sensor group based on the collective impulseresponse, where the FBGs in the array are modeled as a stack of discretereflectors, and the sensor fibers are modeled as transmission delaysbetween the reflectors. With the use of a two-pulse heterodynesub-carrier generation technique, it is possible to calculate theimpulse response of the sensor group, and the layer-peeling algorithmcan be used to calculate the response of the individual sensors withoutcrosstalk. Two or more sensor groups cannot be time division multiplexedon the same fiber because the interrogation pulses reaching the secondgroup have been altered by the transmission through the first group. Ifmore than one sensor group is used, the groups can be multiplexed in thewavelength domain using FBGs as reflectors so that the FBGs of differentsensor groups reflect different wavelengths, while multiple groups atthe same wavelength can be multiplexed by splitting the lead fiber intomultiple fibers using couplers. The split fiber arrangement couplessignal sensor group 124.

As mentioned above, in the array 102, the sensor group consists of fivereflectors 112 ₀ through 112 ₄ and four sensors 110 ₁ through 110 ₄,where the sensors are fibers between each reflector. The Jones matricesρ₀ to ρ₄ represent the amplitude reflectivities of the reflectors, whileB₁, B₂, B₃, B₄ represent the Jones matrices describing the orientationand the phase delays of the polarization eigenmodes of one waytransmission through the sensor fiber. The sensor Jones matrix isdenoted R₁, R₂, R₃, R₄, and is defined as R_(n)=B_(n) ^(T)ρ_(n)B_(n),for n=1, . . . , 4, where T is the matrix transpose operator. Thecommon-mode sensor phase, defined as the mean phase delay of the twoeigenmodes of each sensor is denoted φ₁, φ₂, φ₃, φ₄. The common-modesensor phase φ_(n) of sensor n can be calculated as:φ_(n)=0.5∠det(R _(n))=0.5∠det(B ^(T)ρ_(n) B _(n))=0.5∠(det(B _(n))²det(ρ_(n)))=∠det(B _(n))Here ρ_(n) is chosen so that ∠det(ρ_(n))=0.

Time-division multiplexing of the sensors is achieved using two-pulseheterodyne sub-carrier technique. In one embodiment of the invention,the light source 104 produces two pulses within two time-slots, wherethe time-slots have a length equal to the sensor delay imbalance. Thephase of the second pulse is modulated, which generates a sub-carrier onthe reflected signal. The amplitudes of each pulse in the reflectedpulse train are detected by the light detector 106. At the generatedsub-carrier frequency, both phase and amplitude of the interference aremeasured. While those skilled in the applicable arts will readilycomprehend two-pulse interrogation and demodulation, commonly assignedand co-pending U.S. patent application Ser. No. ______, entitled,“METHOD AND APPARATUS FOR PROVIDING POLARIZATION INSENSITIVE SIGNALPROCESSING FOR INTERFEROMETRIC SENSORS”, which was filed on ______(Attorney Docket Number WEAT/0347), which is hereby incorporated byreference, describes such interrogation techniques in detail.

The visibility of the interference between the first order reflectionand a higher order reflection depends upon the polarization of the twointerfering pulses. If the visibility of this interference is not known,the inverse scattering algorithm will not correctly remove the crosstalkdue to the multiple reflections within the sensor group. It is thereforerequired that the fibers are polarization preserving or that apolarization resolved measurement of the complete Jones matrices foreach time-step of the impulse response is applied. The discussion belowis based on polarization resolved measurement of the impulse response.

FIG. 2 depicts an interrogation pulse pair 200 comprising a first pulse202 and a second pulse 204 as well as a reflected pulse train 206 from asensor group with five reflectors (i.e., four sensors). The length ofthe reflected pulse train 206 from the sensor group is in principleinfinite, due to the multiple reflections within the sensor group. Theinterference between reflections of the two interrogation pulses causesa time varying amplitude for each reflected pulse indicated by thediagonal lines in each pulse 210 through 232. Note that the amplitude ofthe first pulse 208 in the reflected pulse train 206 is constant, sincethis pulse is the reflection of the first interrogation pulse from thefirst reflector, and therefore it has no interference term. The lengthof the pulse train is infinite, however only pulses 210, 212, 214 and216 are needed for demodulation of the phase responses of the fivesensors. The pulses after pulse 216 are called tail pulses, and they donot include any first order reflections. These pulses must fade out toan amplitude given by the maximum allowed crosstalk level before a newpulse train can be received. The length of the tail is given by thereflectivities of the reflectors, and thus the reflectivities limit therepetition rate. The number of pulses that has to be detected in orderto calculate the sensor responses is equal to the number of reflectors.Let the 2×2 complex Jones matrix h_(j) be the j'th sample of the impulseresponse of the group. The electric field phasor of the part of pulse jin the reflected pulse train sequence that is originating from areflection of the first pulse is given byE _(d)(0,j)=h _(j) E _(m)(0)  (1)where E_(m)(0) is the electrical field phasor of the first interrogationpulse. While, the electric field phasor of the part of pulse j in thereflected pulse train sequence that is originating from a reflection ofthe second pulse is given by $\begin{matrix}{{E_{d}\left( {1,j} \right)} = \left\{ \begin{matrix}0 & {{\text{:}j} = 0} \\{h_{j - 1}{E_{m}(1)}} & {{\text{:}j} > 0}\end{matrix} \right.} & (2)\end{matrix}$where E_(m)(1) is the electrical field phasor of the secondinterrogation pulse. h₀ represents the transmission through the leadfiber and the reflection from the first reflector, while h₁ is thetransmission through the lead fiber and the first sensor and thereflection from the second reflector. Relative to h₀, h₁ includesinformation about the state of the first sensor. h₂ includes thetransmission through the lead fiber, first and second sensor, whichgives information about the second sensor. However, h₂ also includes athird order reflection which involves two reflections from firstreflector and one reflection from the second reflector. This term leadsto crosstalk from sensor 1 to sensor 2. The detected power of each pulseof the reflected pulse train sequence is given by, $\begin{matrix}\begin{matrix}{{I(0)} = {{E_{d}^{\dagger}\left( {0,0} \right)}{E_{d}\left( {0,0} \right)}}} \\{= {{{E_{m}^{\dagger}(0)}h_{0}^{\dagger}h_{0}{E_{m}(0)}} = {I_{p}(0)}}}\end{matrix} & (3) \\\begin{matrix}{{I(j)} = {{{E_{d}^{\dagger}\left( {0,j} \right)}{E_{d}\left( {0,j} \right)}} + {{E_{d}^{\dagger}\left( {1,j} \right)}{E_{d}\left( {1,j} \right)}} + {2\quad{Re}\left\{ {{E_{d}^{\dagger}\left( {1,j} \right)}{E_{d}\left( {0,j} \right)}} \right\}}}} \\{= {{{E_{m}^{\dagger}(0)}h_{j}^{\dagger}h_{j}{E_{m}(0)}} + {{E_{m}^{\dagger}(1)}h_{j - 1}^{\dagger}h_{j - 1}{E_{m}(1)}} +}} \\{2\quad{Re}\left\{ {{E_{m}^{\dagger}(1)}h_{j - 1}^{\dagger}h_{j}{E_{m}(0)}} \right\}}\end{matrix} & (4)\end{matrix}$here † is the conjugate transpose operator and I(j) is the measuredpower of the j'th reflected pulse. The detected power is split into thenon-interfering part I_(p)(j), that appears around DC and theinterfering part I_(i)(j) that appears around the sub-carrier frequency.The interfering part is given by,I _(i)(j)=2Re{E _(m) ^(†)(1)H ^((j−1,j)) E _(m)(0)},  (5)where H^((j−1,j))=h_(j)−1^(†)h_(j). The Jones matrix H^((j−1,j)) isdetermined using a polarization resolved measurement method, such as thetechnique described in U.S. patent application Ser. No. ______, filed______ (Attorney Docket Number WEAT/0347).

When H^((j−1,j)) is determined, each sample of the impulse response canbe calculated successively using,h _(j) =h _(j)−1^(†−1) H ^((i−1,j)) =h _(j)−1^(†−1) h ¹⁻¹ ^(†) h_(j,)  (6)where h_(j)−1^(†−1) is the inverse and the conjugate transpose ofh_(j)−1. Equation (6) shows that h₀ is the reference in the successivecalculations. The Jones matrices can be measured in any basis, and thestate of polarization of the interrogation pulses before the firstreflector is chosen as the basis. Then, provided that the polarizationdependence of the reflector reflectivity is negligible, h₀ is a scalartimes the 2×2 identity matrix I, where the scalar is given by the squareroot of the amplitude of the first reflected pulse as defined byequation (3). Thus h₀={square root}{square root over (I_(p)(0))}I.

FIG. 3 depicts a flow diagram of a method 300 that is used in oneembodiment of the present invention for reducing crosstalk interferencewithin an inline FP sensor array. The method 300 begins at step 302 andproceeds to step 304. At step 304, the method 300 transmitsinterrogation pulses into the sensor group. At step 306, the reflectedpulse train is received. The pulse train is processed at step 308 asdescribed above using a first portion of one embodiment of an inversescattering algorithm to determine the impulse response of the sensorgroup. Once the impulse response of the sensor group has beendetermined, a variable n is set to zero (step 310) and the Jonesmatrices describing the reflectors (ρ_(n)) and the fiber sections(B_(n)) can be found using a second portion of the inverse scatteringalgorithm. In other embodiments, the first portion of the inversescattering algorithm involves calculation of the reflection spectrum ofthe sensor group, which is the Fourier transform of the impulseresponse. The reflection spectrum is then the input to the secondportion of the inverse scattering algorithm. In one embodiment, thealgorithm used is the layer-peeling algorithm. The common-mode sensorphase φ_(n) is defined as the phase of the determinant of B_(n), theJones matrix of the fiber section between two reflectors that form asensor. In this embodiment, only the sensor phases are of interest as afinal result, while in other embodiment other properties of B_(n) suchas the differential birefringent phase between the eigenpolarizations orthe orientation of the eigenpolarizations may be extracted. The Jonesmatrices of the reflectors and the fiber sections are required astemporary results in the layer-peeling algorithm. Unless thetransmission through the sensor group is measured, some prior knowledgeabout these matrices are required. From a measurement in reflection, itis not possible to distinguish the reflectivities of the reflectors fromthe loss in the fiber sections. Thus, either the reflectivities of thereflectors are known and polarization independent or the loss in thefiber sections are known and polarization independent. The reflectivityof at least one reflector must be known since usually the loss of thelead fiber, the interrogation power and the detector responsivity arenot known.

The layer-peeling algorithm is based on the assumption that only thereflection from first reflector contributes to the first point in theimpulse response, since all other reflections will have a largertime-delay. From the first point in the impulse response, the matricesdescribing the lead fiber (B₀) and the first reflector (ρ₀) can becomputed at step 312. The sensor phase is calculated as the phase of thedeterminant of B₀ at step 314. However, in the above discussion h₀ waschosen to be a real scalar times the identity matrix, thus also B₀ andρ₀ is be a real scalar times the identity matrix, and the calculatedphase of the lead fiber is zero. At step 316, the transfer matrix of thesection, which relates the forward propagating light u(j) (the impulse)and backward propagating light v(j) (the impulse response) of thissection to the next, can be found from B₀ and ρ₀. Once the transfermatrix is found, at step 318, the optical fields of the forward andbackward propagating light in the next section can be calculated, andthe first reflector is “peeled off”. This procedure removes allreflections involving the first reflector from the measurement. At step320, the method 300 queries whether all the sensor phases have beencomputed. If the query is affirmatively answered, the method 300 stopsat step 324. If the query is negatively answered, the method 300increments the variable n by 1 at step 322 and returns to step 312. Inthe now reduced reflector stack, the second reflector has become thefirst reflector. Thus, the first fiber section matrix (B₁) and thesecond reflector matrix (ρ₁) can be found using the same procedure. Theprocess repeats until all sensor phases are computed. By using thisiterative procedure, the phase of the sensors in the whole sensor groupcan be found without crosstalk.

Below is presented the polarization resolved layer-peeling algorithmthat is used on a sensor group with N+1 reflectors.

-   -   Based on the measurement I_(p)(0), determine the scaling        constant that gives |det h₀|=|det ρ₀|.    -   Scale all components of H^((j−1,j)) with the calculated scale        constant.    -   Calculate h_(j), j=1, . . . , N for a group of N sensors using        (6).

Initialize v(j)=h_(j) for 0≦j≦N, u(0)=I and u(j)=0 for 1≦j≦N  FOR n=0 TON, Calculate R_(n)=B_(n) ^(T)ρ_(n) B_(n)=v(0)u(0)⁻¹ Calculate ρ_(n) andB_(n) from R_(n) Calculate the sensor phase φ_(n)= ∠det B_(n). Calculatethe transfer matrix of section n given by the block matrices: T_(n,11)=B_(n) T_(n,12)=−ρ_(n)B_(n)⁻¹ T_(n,21)=−ρ_(n)B_(n) T_(n,22)=B_(n) ⁻¹ FOR j=0 TO N-n, Propagate thefield matrices to the next section  u(j) = T_(n,11)u(j) + T_(n,12)v(j) v(j) = T_(n,21)u(j + 1) + T_(n,22)v(j + 1)  END ENDHere u and v are the forward and backward propagating field matricesbefore the first fiber section in the reduced reflector stack for eachiteration, respectively. That is, for the first iteration, u and vdescribe the optical fields before the lead fiber, then for the seconditeration, they describe the fields before the fiber section reflector,and so on.

The calculation of ρ_(n) and B_(n) from R_(n) is based on the propertiesof the two matrices ρ_(n) and B_(n). ρ_(n) is a hermittian matrix, whichmeans that it has orthogonal eigenvectors and the eigenvalues are real.B_(n) is a scalar times unitary matrix. A unitary matrix has orthogonaleigenvectors, and the eigenvalues are complex and modulus equal to one.The scalar is given by the loss in the fiber of sensor, and aredetermined by some apriori information about the reflectorreflectivities or the sensor losses. If the sensor fiber includes acomponent of circular birefringence, this component cannot be determinedfrom R_(n). This is because circular birefringence is mathematicallyequivalent to a rotation of the coordinate axes into the reflector.Thus, the circular birefringence cannot be distinguished from theorientation of the eigenvectors of ρ_(n). This does not have anypractical importance, because the reference coordinate system can rotateaccording to the circular birefringence of the fiber sections. If B_(n)is assumed to only describe linear birefringence, the matrix issymmetric, i.e. B_(n) ^(T)=B_(n). The symmetric part of B_(n) and ρ_(n)can be calculated asB _(n)=(R _(n)(R _(n) ^(†) R _(n))^(−1/2) and ρ_(n) =B _(n) ⁻¹ R _(n) B_(n) ⁻¹.

FIG. 4 shows graph 400 of the results of a simulation of the algorithmof a sensor group of five reflectors with reflectivity equal to 3% andfour sensors with arbitrary birefringence. A phase signal of 2 mrad isapplied to the first sensor, while the phase of the other sensors arezero. The measured response is shown as stars, and the response aftercrosstalk elimination with layer-peeling is shown as circles. Thesimulation shows that the algorithm eliminates substantially all thecrosstalk between sensors within a sensor group.

The method can also be used to reduce crosstalk in sensor groups thatare interrogated with signals that use frequency-division multiplexing(FDM), where the laser frequency is swept over a range larger than thefree spectral range of the sensors. Different electrical signalfrequencies are generated at the detector corresponding to differentdelay difference of the two interfering signals. Thus, the interferencesignal components are multiplexed in electrical frequency. To use aninverse scattering algorithm to reduce crosstalk, an FDM based systemuses a reference reflector within the array. FIG. 5 depicts a sensorarray 500 for an FDM system. The sensor array 500 comprises a referencereflector 502 and a sensor group 504. The reference reflector 502 ispositioned a length L, prior to the first reflector 112 ₀ of the sensorgroup 504. In order to extract the impulse response of the sensor group,the length L must be chosen so that reflected signal that appears due tothe interference between the reference reflector and the reflectionsfrom the sensor group is separable from the interference betweenreflections within the sensor group. Thus, the time delay represented bylength L must be longer than the delay at which the amplitude of theimpulse response of the sensor group 504 is faded out to a levelspecified by the allowable crosstalk level. It is also possible toselect a length L so that no delay difference between a reflection fromthe reference reflector and a reflection from the sensor group ismatched by any delay differences between two interfering signals withinthe sensor array. For instance the length L could correspond to half thedistance between two reflectors in a sensor group with uniformly spacedreflectors. In this case it will be interlaced frequencies betweenfrequencies that are generated by the interference between the referencereflector and a reflection from the sensor group, and frequencies thatare generated by interference between reflections within the sensorgroup. Although the depicted embodiment shows the reference reflector502 located in-line with the sensor group 504, the reference may beoff-line and coupled to the sensor group via an optical coupler. Thefrequency of the interference between the reference reflector 502 and areflection from the sensor group 504 depends on the time-delay of thesensor group reflection since the laser is swept, and thus the sensorsare multiplexed in electrical frequency. The crosstalk in such aconfiguration is the same as for the TDM case. The impulse response iscalculated using the inverse Fourier transform, and the crosstalk can beeliminated using an inverse scattering algorithm.

While the foregoing is directed to the preferred embodiment of thepresent invention, other and further embodiments of the invention may bedevised without departing from the basic scope thereof, and the scopethereof is determined by the claims that follow.

1. A method for detecting sensor phase in an optical, interferometricsensor array comprising: transmitting an interrogation signal into asensor array of sensor elements and a plurality of spaced apart inlinereflector sensors, wherein each sensor element comprising the opticaltransmission path between two inline reflectors; receiving a reflectedsignal from the sensor array; and applying an inverse scatteringalgorithm to the reflected signal to reduce crosstalk interference. 2.The method of claim 1 further including determining a signal phase delayresponse of a sensor element.
 3. The method of claim 1 further includingdetermining a common mode phase response of a sensor element.
 4. Themethod of claim 1 further including determining a differentialbirefringent response of a sensor element.
 5. The method of claim 1wherein the interrogation signal comprises at least one signal pulse. 6.The method of claim 1 wherein the interrogation signal comprises asignal having a varying frequency.
 7. The method of claim 1 wherein theinverse scattering algorithm comprises: (a) determining Jones matricesfor the sensors in the sensor array; (b) computing a sensor response fora sensor in the sensor array; (c) computing a transfer matrix; (d)determining the forward and backward propagating optical fields from thesensor; and (e) repeating steps (a), (b), (c) and (d) for each sensor inthe sensor array.
 8. The method of claim 7 wherein the sensor responseincludes a signal phase delay response.
 9. The method of claim 7 whereinthe sensor response includes a common mode phase response.
 10. Themethod of claim 7 wherein the sensor response includes a differentialbirefringent phase response.
 11. The method of claim 1 wherein theinverse scattering algorithm comprises: computing from the reflectedsignal an impulse response of the sensor array; and using the impulseresponse to define parameters of the inverse scattering algorithm. 12.Apparatus for detecting sensor phase in a sensor array comprising: alight source for transmitting an interrogation signal into a sensorarray having a plurality of spaced apart inline reflector sensors; alight detector for receiving a reflected signal from the sensor array; asignal processor for applying an inverse scattering algorithm to thereflected signal that reduces crosstalk interference.
 13. The apparatusof claim 12 wherein the signal processor further determines a signalphase delay response between a pair of line reflector sensors.
 14. Theapparatus of claim 12 wherein the signal processor further determines acommon mode phase response of a pair of line reflector sensors.
 15. Theapparatus of claim 12 wherein the signal processor further determines adifferential birefringent response of a pair of line reflector sensors.16. The apparatus of claim 12 wherein the interrogation signal comprisesat least one signal pulse.
 17. The apparatus of claim 12 wherein theinterrogation signal comprises a signal having a varying frequency. 18.The apparatus of claim 12 wherein the inverse scattering algorithmcomputes an impulse response of the sensor array from the reflectedsignal, and then uses the impulse response to define parameters of theinverse scattering algorithm.
 19. A computer readable medium comprisingsoftware that, when executed by a processor, causes the processor toprocess signals reflected from a sensor array using a method comprising:(a) determining Jones matrices for a sensor within the sensor array; (b)computing a sensor phase for the sensor; (c) computing a transfermatrix; (d) determining the forward and backward propagating opticalfields from the sensor; and (e) repeating steps (a), (b), (c) and (d)for each other sensor in the sensor array.